1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

1.2 The Data

DARWIN <- read.csv("~/GitHub/FCA/Data/DARWIN/DARWIN.csv")
rownames(DARWIN) <- DARWIN$ID
DARWIN$ID <- NULL
DARWIN$class <- 1*(DARWIN$class=="P")
print(table(DARWIN$class))
#> 
#>  0  1 
#> 85 89

DARWIN[,1:ncol(DARWIN)] <- sapply(DARWIN,as.numeric)

signedlog <- function(x) { return (sign(x)*log(abs(1.0e12*x)+1.0))}
whof <- !(colnames(DARWIN) %in% c("class"));
DARWIN[,whof] <- signedlog(DARWIN[,whof])

1.2.0.1 Standarize the names for the reporting

studyName <- "DARWIN"
dataframe <- DARWIN
outcome <- "class"

TopVariables <- 10

thro <- 0.80
cexheat = 0.15

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))
rows col
174 450
pander::pander(table(dataframe[,outcome]))
0 1
85 89

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns


  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data


if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9994118

1.5 The decorrelation


DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  gmrt_on_paper5 mean_jerk_on_paper14 mean_jerk_on_paper16 gmrt_on_paper18 mean_jerk_on_paper3 mean_acc_in_air25 
#>        air_time1      disp_index1     gmrt_in_air1   gmrt_on_paper1 
#>       0.43777778       0.48222222       0.49111111       0.79333333 
#> max_x_extension1 max_y_extension1 
#>       0.02222222       0.15111111 
#> 
#>  Included: 450 , Uni p: 0.0003333333 , Base Size: 21 , Rcrit: 0.2555213 
#> 
#> 
 1 <R=0.945,thr=0.950>, Top: 75< 9 >[Fa= 75 ]( 75 , 131 , 0 ),<|><>Tot Used: 206 , Added: 131 , Zero Std: 0 , Max Cor: 0.990
#> 
 2 <R=0.893,thr=0.950>, Top: 5< 3 >[Fa= 80 ]( 5 , 7 , 75 ),<|><>Tot Used: 212 , Added: 7 , Zero Std: 0 , Max Cor: 0.950
#> 
 3 <R=0.888,thr=0.900>, Top: 39< 1 >[Fa= 104 ]( 37 , 39 , 80 ),<|><>Tot Used: 260 , Added: 39 , Zero Std: 0 , Max Cor: 0.919
#> 
 4 <R=0.862,thr=0.900>, Top: 3< 1 >[Fa= 104 ]( 3 , 3 , 104 ),<|><>Tot Used: 260 , Added: 3 , Zero Std: 0 , Max Cor: 0.899
#> 
 5 <R=0.860,thr=0.800>, Top: 50< 1 >[Fa= 135 ]( 48 , 60 , 104 ),<|><>Tot Used: 327 , Added: 60 , Zero Std: 0 , Max Cor: 0.874
#> 
 6 <R=0.837,thr=0.800>, Top: 12< 1 >[Fa= 144 ]( 12 , 12 , 135 ),<|><>Tot Used: 336 , Added: 12 , Zero Std: 0 , Max Cor: 0.926
#> 
 7 <R=0.880,thr=0.900>, Top: 1< 1 >[Fa= 144 ]( 1 , 1 , 144 ),<|><>Tot Used: 336 , Added: 1 , Zero Std: 0 , Max Cor: 0.887
#> 
 8 <R=0.869,thr=0.800>, Top: 2< 1 >[Fa= 144 ]( 2 , 2 , 144 ),<|><>Tot Used: 336 , Added: 2 , Zero Std: 0 , Max Cor: 0.799
#> 
 9 <R=0.799,thr=0.800>
#> 
 [ 9 ], 0.79919 Decor Dimension: 336 Nused: 336 . Cor to Base: 209 , ABase: 450 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

692

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

135

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

4.57

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

4.45


varratio <- attr(DEdataframe,"VarRatio")

pander::pander(tail(varratio))
La_mean_acc_on_paper14 La_max_x_extension5 La_mean_jerk_in_air25 La_mean_jerk_in_air17 La_mean_speed_on_paper5 La_mean_speed_on_paper12
0.00256 0.00219 0.00218 0.00133 0.00118 0.000866

1.5.1 The decorrelation matrix


if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPLTM <- attr(DEdataframe,"UPLTM")
  
  gplots::heatmap.2(1.0*(abs(UPLTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
  
  
  
}

1.5.2 Formulas Network

Displaying the features associations

par(op)
clustable <- c("To many variables")


  transform <- attr(DEdataframe,"UPLTM") != 0
  tnames <- colnames(transform)
  colnames(transform) <- str_remove_all(colnames(transform),"La_")
  transform <- abs(transform*cor(dataframe[,rownames(transform)])) # The weights are proportional to the observed correlation
  
  
  fscore <- attr(DEdataframe,"fscore")
  VertexSize <- fscore # The size depends on the variable independence relevance (fscore)
  names(VertexSize) <- str_remove_all(names(VertexSize),"La_")
  VertexSize <- 10*(VertexSize-min(VertexSize))/(max(VertexSize)-min(VertexSize)) # Normalization

  VertexSize <- VertexSize[rownames(transform)]
  rsum <- apply(1*(transform !=0),1,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  csum <- apply(1*(transform !=0),2,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  
  ntop <- min(10,length(rsum))


  topfeatures <- unique(c(names(rsum[order(-rsum)])[1:ntop],names(csum[order(-csum)])[1:ntop]))
  rtrans <- transform[topfeatures,]
  csum <- (apply(1*(rtrans !=0),2,sum) > 1*(colnames(rtrans) %in% topfeatures))
  rtrans <- rtrans[,csum]
  topfeatures <- unique(c(topfeatures,colnames(rtrans)))
  print(ncol(transform))

[1] 336

  transform <- transform[topfeatures,topfeatures]
  print(ncol(transform))

[1] 90

  if (ncol(transform)>100)
  {
    csum <- apply(1*(transform !=0),1,sum) 
    csum <- csum[csum > 1]
    csum <- csum + 0.01*VertexSize[names(csum)]
    csum <- csum[order(-csum)]
    tpsum <- min(20,length(csum))
    trsum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
    rtrans <- transform[trsum,]
    topfeatures <- unique(c(rownames(rtrans),colnames(rtrans)))
    transform <- transform[topfeatures,topfeatures]
    if (nrow(transform) > 150)
    {
      csum <- apply(1*(rtrans != 0 ),2,sum)
      csum <- csum + 0.01*VertexSize[names(csum)]
      csum <- csum[order(-csum)]
      tpsum <- min(130,length(csum))
      csum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
      csum <- unique(c(trsum,csum))
      transform <- transform[csum,csum]
    }
    print(ncol(transform))
  }

    if (ncol(transform) < 150)
    {

      gplots::heatmap.2(transform,
                        trace = "none",
                        mar = c(5,5),
                        col=rev(heat.colors(5)),
                        main = "Red Decorrelation matrix",
                        cexRow = cexheat,
                        cexCol = cexheat,
                       srtCol=45,
                       srtRow=45,
                        key.title=NA,
                        key.xlab="|Beta|>0",
                        xlab="Output Feature", ylab="Input Feature")
  
      par(op)
      VertexSize <- VertexSize[colnames(transform)]
      gr <- graph_from_adjacency_matrix(transform,mode = "directed",diag = FALSE,weighted=TRUE)
      gr$layout <- layout_with_fr
      
#      fc <- cluster_optimal(gr)
        fc <- cluster_walktrap (gr,steps=50)
      plot(fc, gr,
           edge.width = 2*E(gr)$weight,
           vertex.size=VertexSize,
           edge.arrow.size=0.5,
           edge.arrow.width=0.5,
           vertex.label.cex=(0.15+0.05*VertexSize),
           vertex.label.dist=0.5 + 0.05*VertexSize,
           main="Top Feature Association")
      
      varratios <- varratio
      fscores <- fscore
      names(varratios) <- str_remove_all(names(varratios),"La_")
      names(fscores) <- str_remove_all(names(fscores),"La_")

      dc <- getLatentCoefficients(DEdataframe)
      theCharformulas <- attr(dc,"LatentCharFormulas")

      
      clustable <- as.data.frame(cbind(Variable=fc$names,
                                       Formula=as.character(theCharformulas[paste("La_",fc$names,sep="")]),
                                       Class=fc$membership,
                                       ResidualVariance=round(varratios[fc$names],3),
                                       Fscore=round(fscores[fc$names],3)
                                       )
                                 )
      rownames(clustable) <- str_replace_all(rownames(clustable),"__","_")
      clustable$Variable <- NULL
      clustable$Class <- as.integer(clustable$Class)
      clustable$ResidualVariance <- as.numeric(clustable$ResidualVariance)
      clustable$Fscore <- as.numeric(clustable$Fscore)
      clustable <- clustable[order(-clustable$Fscore),]
      clustable <- clustable[order(clustable$Class),]
      clustable <- clustable[clustable$Fscore >= -1,]
      topv <- min(50,nrow(clustable))
      clustable <- clustable[1:topv,]
    }


pander::pander(clustable)
  Formula Class ResidualVariance Fscore
gmrt_on_paper12 NA 1 1.000 7
paper_time12 - (1.034)gmrt_on_paper12 + paper_time12 1 0.115 5
mean_acc_on_paper12 - (0.768)gmrt_on_paper12 + mean_acc_on_paper12 1 0.033 0
disp_index12 + disp_index12 - (0.438)paper_time12 1 0.019 -1
max_x_extension12 - (1.034)gmrt_on_paper12 + max_x_extension12 1 0.032 -1
num_of_pendown12 + num_of_pendown12 - (0.795)paper_time12 1 0.084 -1
pressure_var12 - (1.064)paper_time12 + pressure_var12 1 0.085 -1
gmrt_on_paper18 NA 2 1.000 9
disp_index18 + disp_index18 - (0.452)gmrt_on_paper18 2 0.101 3
mean_jerk_on_paper18 - (0.707)gmrt_on_paper18 + mean_jerk_on_paper18 2 0.020 0
mean_speed_on_paper18 - (0.882)gmrt_on_paper18 + mean_speed_on_paper18 2 0.004 -1
pressure_mean18 - (1.044)gmrt_on_paper18 + pressure_mean18 2 0.026 -1
pressure_var18 - (1.161)gmrt_on_paper18 + pressure_var18 2 0.083 -1
mean_jerk_on_paper3 NA 3 1.000 10
gmrt_on_paper3 + gmrt_on_paper3 - (1.382)mean_jerk_on_paper3 3 0.033 1
paper_time3 - (1.561)mean_jerk_on_paper3 + paper_time3 3 0.022 0
max_x_extension3 + max_x_extension3 - (1.537)mean_jerk_on_paper3 3 0.023 -1
max_y_extension3 + max_y_extension3 - (1.448)mean_jerk_on_paper3 3 0.055 -1
mean_acc_on_paper3 + mean_acc_on_paper3 - (1.092)mean_jerk_on_paper3 3 0.004 -1
num_of_pendown3 - (1.221)mean_jerk_on_paper3 + num_of_pendown3 3 0.047 -1
pressure_mean3 - (1.501)mean_jerk_on_paper3 + pressure_mean3 3 0.011 -1
pressure_var3 - (1.672)mean_jerk_on_paper3 + pressure_var3 3 0.035 -1
mean_jerk_on_paper16 NA 4 1.000 10
gmrt_on_paper16 + gmrt_on_paper16 - (1.376)mean_jerk_on_paper16 4 0.032 0
max_y_extension16 + max_y_extension16 - (1.494)mean_jerk_on_paper16 4 0.037 0
paper_time16 - (1.484)mean_jerk_on_paper16 + paper_time16 4 0.068 0
mean_acc_on_paper16 + mean_acc_on_paper16 - (1.089)mean_jerk_on_paper16 4 0.004 -1
num_of_pendown16 - (1.227)mean_jerk_on_paper16 + num_of_pendown16 4 0.082 -1
pressure_mean16 - (1.467)mean_jerk_on_paper16 + pressure_mean16 4 0.024 -1
pressure_var16 - (1.670)mean_jerk_on_paper16 + pressure_var16 4 0.054 -1
mean_jerk_on_paper2 NA 5 1.000 10
gmrt_on_paper2 + gmrt_on_paper2 - (1.369)mean_jerk_on_paper2 5 0.058 0
max_y_extension2 + max_y_extension2 - (1.544)mean_jerk_on_paper2 5 0.021 0
paper_time2 - (1.572)mean_jerk_on_paper2 + paper_time2 5 0.043 0
max_x_extension2 + max_x_extension2 - (1.465)mean_jerk_on_paper2 5 0.071 -1
mean_acc_on_paper2 + mean_acc_on_paper2 - (1.092)mean_jerk_on_paper2 5 0.008 -1
num_of_pendown2 - (1.250)mean_jerk_on_paper2 + num_of_pendown2 5 0.105 -1
pressure_var2 - (1.684)mean_jerk_on_paper2 + pressure_var2 5 0.066 -1
mean_speed_on_paper21 NA 6 1.000 4
mean_acc_on_paper21 + mean_acc_on_paper21 + (0.602)mean_speed_on_paper21 6 0.297 0
paper_time21 + (0.912)mean_speed_on_paper21 + paper_time21 6 0.347 0
disp_index21 + disp_index21 - (0.855)mean_speed_on_paper21 - (0.937)paper_time21 6 0.275 -1
gmrt_on_paper21 + gmrt_on_paper21 - (0.939)mean_speed_on_paper21 6 0.055 -1
total_time21 + (1.007)mean_speed_on_paper21 + total_time21 6 0.263 -1
mean_jerk_on_paper14 NA 7 1.000 10
gmrt_on_paper14 + gmrt_on_paper14 - (1.391)mean_jerk_on_paper14 7 0.020 0
paper_time14 - (1.527)mean_jerk_on_paper14 + paper_time14 7 0.036 0
max_x_extension14 + max_x_extension14 - (1.506)mean_jerk_on_paper14 7 0.051 -1
max_y_extension14 + max_y_extension14 - (1.526)mean_jerk_on_paper14 7 0.040 -1
mean_acc_on_paper14 + mean_acc_on_paper14 - (1.091)mean_jerk_on_paper14 7 0.003 -1

par(op)

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after ILAA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.79919

1.8 U-MAP Visualization of features

1.8.1 The UMAP on Raw Data


  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  topvars <- univariate_BinEnsemble(dataframe,outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),dataframe,family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

air_time17, total_time17, air_time23, total_time23, air_time7 and total_time15

#  names(topvars)
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(dataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(dataframe[1:numsub,varlist],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])

#}

1.8.2 The decorralted UMAP

  varlistcV <- names(varratio[varratio >= 0.01])
  topvars <- univariate_BinEnsemble(DEdataframe[,varlistcV],outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),DEdataframe[,varlistcV],family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

air_time17, total_time23, total_time15, total_time6, total_time7 and mean_acc_in_air17


  varlistcV <- varlistcV[varlistcV != outcome]
  
#  DEdataframe[,outcome] <- as.numeric(DEdataframe[,outcome])
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(DEdataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(DEdataframe[1:numsub,varlistcV],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After ILAA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])

#}

1.9 Univariate Analysis

1.9.1 Univariate



univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : mean_jerk_in_air6 200 : disp_index12 300 : mean_speed_in_air17 400 : gmrt_on_paper23




univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : La_mean_jerk_in_air6 200 : La_disp_index12 300 : La_mean_speed_in_air17 400 : La_gmrt_on_paper23

1.9.2 Final Table


univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)
  caseMean caseStd controlMean controlStd controlKSP ROCAUC
total_time23 37.2 0.503 36.7 0.484 1.03e-05 0.863
total_time15 38.1 0.875 37.1 0.421 5.44e-01 0.844
air_time23 36.6 0.626 35.9 0.656 6.92e-03 0.844
air_time15 37.7 1.094 36.6 0.615 5.06e-01 0.829
total_time17 38.5 0.681 37.8 0.614 4.00e-03 0.824
paper_time23 36.4 0.439 36.0 0.231 6.72e-01 0.814
air_time17 37.9 0.914 37.0 0.795 3.52e-02 0.806
paper_time17 37.6 0.395 37.2 0.439 1.28e-03 0.796
total_time6 37.1 0.777 36.4 0.447 7.16e-01 0.790
air_time16 36.4 1.131 35.2 0.867 9.38e-01 0.787


topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)
  caseMean caseStd controlMean controlStd controlKSP ROCAUC
total_time23 37.2307 0.503 36.666 0.484 1.03e-05 0.863
total_time15 38.0918 0.875 37.146 0.421 5.44e-01 0.844
air_time17 37.9116 0.914 37.000 0.795 3.52e-02 0.806
paper_time17 37.6037 0.395 37.205 0.439 1.28e-03 0.796
total_time6 37.1004 0.777 36.368 0.447 7.16e-01 0.790
air_time16 36.3573 1.131 35.240 0.867 9.38e-01 0.787
total_time7 37.1660 0.690 36.578 0.812 1.87e-03 0.785
total_time22 37.2925 0.783 36.656 0.346 5.74e-01 0.780
gmrt_in_air7 32.9484 0.405 33.382 0.396 9.99e-01 0.775
total_time9 37.0580 0.769 36.334 0.482 7.12e-01 0.774
La_pressure_var5 1.2955 1.270 0.409 0.837 4.47e-01 0.738
La_pressure_mean2 0.0214 0.298 0.219 0.156 7.30e-02 0.737
La_disp_index17 -35.4440 0.142 -35.557 0.134 1.61e-01 0.731
La_gmrt_on_paper2 0.3429 0.605 0.821 0.488 7.04e-01 0.725
La_paper_time23 57.6825 0.224 57.508 0.204 8.41e-01 0.723

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))
mean total fraction
2.17 221 0.491

theCharformulas <- attr(dc,"LatentCharFormulas")

topvar <- rownames(tableRaw)
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
finalTable$varratio <- varratio[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores","varratio")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])
  DecorFormula caseMean caseStd controlMean controlStd controlKSP ROCAUC RAWAUC fscores varratio
total_time23 NA 37.2307 0.503 36.666 0.484 1.03e-05 0.863 0.863 1 1.00000
total_time15 NA 38.0918 0.875 37.146 0.421 5.44e-01 0.844 0.844 1 1.00000
air_time23 NA 36.6116 0.626 35.858 0.656 6.92e-03 0.844 0.844 NA NA
air_time15 NA 37.7203 1.094 36.607 0.615 5.06e-01 0.829 0.829 NA NA
total_time17 NA 38.5262 0.681 37.848 0.614 4.00e-03 0.824 0.824 NA NA
paper_time23 NA 36.4011 0.439 36.001 0.231 6.72e-01 0.814 0.814 NA NA
air_time17 NA 37.9116 0.914 37.000 0.795 3.52e-02 0.806 0.806 1 1.00000
paper_time17 NA 37.6037 0.395 37.205 0.439 1.28e-03 0.796 0.796 0 1.00000
total_time6 NA 37.1004 0.777 36.368 0.447 7.16e-01 0.790 0.790 1 1.00000
air_time16 NA 36.3573 1.131 35.240 0.867 9.38e-01 0.787 0.787 1 1.00000
total_time7 NA 37.1660 0.690 36.578 0.812 1.87e-03 0.785 0.785 1 1.00000
total_time22 NA 37.2925 0.783 36.656 0.346 5.74e-01 0.780 0.780 1 1.00000
gmrt_in_air7 NA 32.9484 0.405 33.382 0.396 9.99e-01 0.775 0.775 1 1.00000
total_time9 NA 37.0580 0.769 36.334 0.482 7.12e-01 0.774 0.774 2 1.00000
La_pressure_var5 - (1.169)gmrt_on_paper5 + pressure_var5 1.2955 1.270 0.409 0.837 4.47e-01 0.738 0.274 -1 0.07763
La_pressure_mean2 - (0.970)max_y_extension2 + (3.71e-03)mean_jerk_on_paper2 + pressure_mean2 0.0214 0.298 0.219 0.156 7.30e-02 0.737 0.312 -2 0.00938
La_disp_index17 + disp_index17 - (1.415)max_y_extension17 -35.4440 0.142 -35.557 0.134 1.61e-01 0.731 0.736 -1 0.26605
La_gmrt_on_paper2 + gmrt_on_paper2 - (1.369)mean_jerk_on_paper2 0.3429 0.605 0.821 0.488 7.04e-01 0.725 0.337 0 0.05839
La_paper_time23 + (0.746)mean_speed_on_paper23 + paper_time23 57.6825 0.224 57.508 0.204 8.41e-01 0.723 0.814 0 0.32434

1.10 Comparing ILAA vs PCA vs EFA

1.10.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE,tol=0.01)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

1.10.2 EFA


EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)-1)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

1.11 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }


pander::pander(table(dataframe[,outcome],pr))
  0 1
0 78 7
1 7 82
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.920 0.869 0.955
3 se 0.921 0.845 0.968
4 sp 0.918 0.838 0.966
6 diag.or 130.531 43.775 389.223

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe[,c(outcome,varlistcV)],control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="ILAA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))
  0 1
0 74 11
1 5 84
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.908 0.855 0.947
3 se 0.944 0.874 0.982
4 sp 0.871 0.780 0.934
6 diag.or 113.018 37.532 340.322

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))
  0 1
0 65 20
1 2 87
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.874 0.815 0.919
3 se 0.978 0.921 0.997
4 sp 0.765 0.660 0.850
6 diag.or 141.375 31.905 626.443


par(op)

1.11.1 EFA


  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }


  pander::pander(table(EFAdataframe[,outcome],pr))
  0 1
0 80 5
1 33 56
  pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.782 0.713 0.841
3 se 0.629 0.520 0.729
4 sp 0.941 0.868 0.981
6 diag.or 27.152 9.982 73.854
  par(op)